[bayes]

I was quite excited when I saw that New Scientist - generally a pretty good magazine - had a piece on the maths of gambling. But unfortunately it turned out to be an extremely poor article.

The first three sections - on card counting, choosing unpopular lottery numbers and arbitrage - skim very briefly over well-known subject matter.

The fourth section is completely wrong - it applies the maths of a situation where you see a number of opportunities in turn until you choose one (e.g. choosing a marriage partner) to the problem of choosing when to stop gambling (where it doesn't apply at all), and draws nonsensical conclusions as a result.

The fact it was written by New Scientist's career editor is telling I suspect.

[secret]

I was going to post this as an "Ask HN", but since I see someone with the username bayes writing in a probability thread- I figure why not ask here (if its all a coincidence, sorry!)

Would you happen to have a recommendation for a good probability textbook for a first year grad student?

[bayes]

I'm afraid my username doesn't reflect any deep knowledge of the field. I studied probability at an undergraduate level many years ago, and still use it in my hobby (writing 'bots' that run automated trading strategies on one of the sports betting exchanges here in the UK), but that's all. I'd go for an "Ask HN" thread if I were you.

[secret]

Thanks anyway. I figured it was worth a shot.

[req2]

I've asked this question before, and though I haven't gotten to the point where I could direct you to the best place to start, it would probably be in one of these books:

E.T. Jaynes, "Probability Theory: The Logic of Science"

Judea Pearl, "Probabilistic Reasoning in Intelligent Systems"

Bayesian Data Analysis, 2nd ed by Gelman et. al